So, syntactically speaking "My" question vs "this" question doesn't actually change anything about the example that I'm making. If making my example analogy closer to the question in the picture will help you understand the point, I can do that too, no worries.

So, let us word it like this then

"Is the answer to this question a bear, a moose, a lion, or a tiger?"

The question fails before it reaches the stage where an answer is chosen, because the question is not formatted correctly. It is nonsensical to attempt to determine which of the four animals is the answer to the question, because the question is a nonsense question.

In the same way, while it is a clever way to set up a question to imply a paradox, while it is a very fun way to contemplate how the answer might change given how the 'correct' answer changes based on which answer you choose; the reality of the situation is that the question actually fails before reaching the 'choose an answer' stage of the problem, because the self-referential language makes the question itself nonsensical.

Is that clearer?